1. (Field of the Invention)
The present invention relates to a frequency demodulator used in, for example, a video tape recorder, for further demodulating a signal that has been converted from an analog frequency-modulated (FM) signal into a digital signal.
2. (Description of the Prior Art)
It is well known that when an analog FM signal X(t) at a certain time t is frequency-demodulated, the resultant frequency-demodulated signal F(t) has the following relationship: ##EQU1## wherein Y(t) represents the analog FM signal which is shifted 90.degree. in phase from the phase of the analog FM signal X(t) at the certain time t. The term tan.sup.-1 [X(t)/Y(t)] of equation (1) is descriptive of the phase of the frequency-modulated wave, and when this term of the equation (1) is expressed by .phi.(t), equation (1) can be rewritten as follows: ##EQU2##
FIG. 3 of the accompanying drawings illustrates a prior art frequency demodulator which utilizes a digital signal processing technology that permits it to operate according to the equation (2).
Referring now to FIG. 3 the frequency demodulator comprises an analog-to-digital converter 1 having a sampling cycle T for converting an inputted analog FM signal into a digital signal. The digital FM signal outputted from the analog-to-digital converter 1 is supplied to a 90.degree. phase shifter 3 which phase shifts the digital FM signal by 90.degree. relative to the input to the phase shifter 3, thereby providing signal Y. The digital FM signal outputted from the analog-to-digital converter 1 is also supplied to a delay compensator 2 for delaying the input digital FM signal for a length of time during which the digital FM signal applied to the phase shifter 3 is shifted in phase. This delay circuit provides a delayed digital FM signal X. The delayed digital FM signal X and the phase-shifted digital FM signal Y are recognized as signals which have been quantified at the same time. Both the delayed and phase-shifted digital FM signals X and Y from the delay compensator 2 and the phase shifter 3, respectively, are applied to a calculator 4 adapted to perform a calculation of tan.sup.-1 (X/Y) with respect to both of these input signals X and Y. An output from the calculator 4 is applied in part to a delay circuit 5 for delaying the output from the calculator 4 for a length of time equal to one sampling cycle T, and in part to a subtractor 6 for subtracting the delayed output of the delay circuit 5 from the output of the calculator 4.
Specifically, the calculator 4 used in the prior art frequency demodulator utilizes a read-only memory which is addressable by the delayed and phase-shifted digital FM signals X and Y. The memory stores, as memory content, the arc tangent (tan.sup.-1) values associated with (X/Y). With this construction, the calculator can provide, as an output, a signal representative of tan.sup.-1 (X/Y) in response to the delayed and phase-shifted digital FM signals X and Y received from the delay compensator 2 and the phase shifter 3, respectively.
The output from the calculator 4 represents the function .phi.(K.T) the frequency modulated wave at time t=K.T as described above. For the purpose of simplification, if the function .phi.(K.T) is expressed by .phi.(K) (Hereinafter, other than .phi.(K), a similar nomenclature is employed), the output from the delay circuit 5 is expressed by .phi.(K-1) and the output from the subtractor 6 is expressed by .phi.(K)-.phi.(K-1). This difference is expressed by .DELTA..phi.(K).
Where the sampling cycle T is sufficiently small, the equation (2) above can be approximated as follows: EQU F(K).apprxeq.[.DELTA..phi.(K)]/T (3)
Since the sampling cycle T is fixed, as is understood from the equation (3) above, the output .DELTA..phi.(K) from the subtractor 6 is similar to the demodulated signal F(K), and in this sense, the output from the subtractor can be regarded as a demodulated signal.
However, the arc tangent is a cyclic function, and assuming that when the cycle is 2.pi. with due regard paid to the sign taken by each of the delayed and phase-shifted digital FM signals X and Y, a table in the read-only memory has values from zero to 2.pi.. When .phi.(K-1) and .phi.(K) are 1.9.pi. and 2.1.pi., respectively, as true outputs of tan.sup.-1 (X/Y), the output from the calculator 4 is such that .phi.(K-1) remains unchanged, that is, .phi.(K-1)=1.9.pi., and .phi.(K) will become 0.1.pi.. Therefore, a problem tends to occur in that the output from the subtractor 6, that is, [.phi.(K)-.phi.(K-1)], may take a negative value (-1.8.pi.), thereby inviting a discontinuity in the output.
In view of the foregoing problem, a discontinuity corrector 7 is employed for performing a correction such that when the output from the subtractor 6 takes a negative value, 2.pi. is added to the negative output from the subtractor 6. With this discontinuity corrector 7, whenever the output from the subtractor 6 takes a negative value, the discontinuity corrector 7 can provide properly corrected outputs from the subtractor 6 with no discontinuity. The output from the discontinuity corrector 7 is expressed by S1(K). When the output from the discontinuity corrector 7 is subsequently converted by a digital-to-analog converter 9, the frequency demodulated signal, which is the input signal whose frequency has been demodulated, can be obtained.
It has, however, been found that the prior art frequency demodulator shown in FIG. 3 has a problem. In particular, when the input FM signal supplied to the analog-to-digital converter 1 is an unbalanced frequency modulated wave generally used in a luminance signal reproduction system such as a home video tape recorder and an upper side-band of the FM wave is suppressed and a lower side-band of the same FM wave is enhanced, it has been experimentally found that the frequency demodulated signal outputted from the frequency demodulator often jumps out of a permissible tolerance level with the consequence that the demodulated output is reversed to the black or white side. If this frequency modulated wave is outputted through the digital-to-analog converter and is then reproduced on a screen of a cathode ray tube, discrete lines of black or white color extending along the horizontal scanning lines appear, thereby creating a problem associated with the reproduced picture on the screen.